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2 years ago

Solve LaTeX: \frac{-x}{3}<5

Mathematics

2 answers:

spayn [35]2 years ago

7 0

Answer:

Step-by-step explanation:

I am Lyosha [343]2 years ago

3 0

Answer:

x > -15

Step-by-step explanation:

-x / 3 < 5

(-x / 3) * 3 < 5 * 3

-x < 15

x > -15 (Remember to flip the sign when multiplying or dividing an inequality by a negative number.)

You might be interested in

How do you Simplify 16/12

vlada-n [284]

You need to find a common factor that both the numerator and denominator have. 16 and 12 have common divisible factors of 2 and 4(excluding 1, because 1 is self-defined but doesn't simplify values at all).

We use the highest factor, in this case, 4.

Divide 16 by 4 and 12 by 4.

16/4 = 4
12/4 = 3

We put 4 in place of the numerator and 3 in place of the denominator.

$\frac{4}{3}$

4 0

2 years ago

Read 2 more answers

What is the area of the composite figure? (use 3.14 for pi). Explain how you arrived at your answer. Please round to the nearest

maksim [4K]

The area of the given diagram is 29.817 square centimeters. The given diagram is combination of rectangle and semi circle.

Step-by-step explanation:

The given is,

Given diagram is combination of Rectangle and Semi circle.

Step:1

Res the attachment,

Area of given diagram = Area of A + Area of B..............(1)

Step:2

For A,

The A section in the given diagram is semi circle,

Diameter of semi circle = Total distance - ( 2+3)

( ∵ 2, 3 are top distance in the given diagram)

$= 10 - 5$

Diameter, d = 5 cm

Radius, $r = \frac{d}{2}$

$r = \frac{5}{2}$

r = 2.5 cm

Area, $A_{A} = \frac {\pi r^{2} }{2}$ ........................(2)

$A_{A} = \frac {\pi (2.5)^{2} }{2}$

$= \frac {\pi ( 6.25) }{2}$

$= \frac{19.63}{2}$

$A_{A} = 9.8174 cm^{2}$

Step:3

For B,

Area of rectangle is,

$A_{B} =lb$ .....................(3)

Where, l - Length = 10 cm

b - Width = 2 cm

Equation (3) become,

$= (10)(2)$

$= 20$

Area of B, $A_{B}$ = 20 $cm^{2}$

Step:4

From the equation (1),

Area of given diagram = 20+ 9.81747

Area = 29.817 square centimeters

Result:

The area of the given diagram is 29.817 square centimeters. The given diagram is combination of rectangle and semi circle.

5 0

2 years ago

The National Cancer Institute estimates that 3.65% of women in their 60s get breast cancer. A mammogram can typically identify c

masha68 [24]

Answer:

39.17% probability that a woman in her 60s who has a positive test actually has breast cancer

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)}$

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Positive test.

Event B: Having breast cancer.

3.65% of women in their 60s get breast cancer

This means that $P(B) = 0.0365$

A mammogram can typically identify correctly 85% of cancer cases

This means that $P(A|B) = 0.85$

Probability of a positive test.

85% of 3.65% and 100-95 = 5% of 100-3.65 = 96.35%. So

$P(A) = 0.85*0.0365 + 0.05*0.9635 = 0.0792$

What is the probability that a woman in her 60s who has a positive test actually has breast cancer?

$P(B|A) = \frac{0.0365*0.85}{0.0792} = 0.3917$

39.17% probability that a woman in her 60s who has a positive test actually has breast cancer

7 0

2 years ago

The larger of two positive integers is three more than the

katrin2010 [14]

Answer:

y=x+4

Step-by-step explanation:

So, let's start with the fact that we have two numbers. Let's call one of them "x" and the other one "y." Let's also assume that "y" is the larger number and "x" is the smaller number.

We know that both of them added together (the sum) gives us 74. Mathematically, that means:

x+y=74.

We also know that the larger number ("y") is 4 more than the smaller number ("x"). Another way to say this is, if you have the smaller number and add 4 more to it, you'll end up with the larger number. Mathematically, this means:

y=x+4

Since we know that y=x+4, we can put "x+4" into the first equation for "y", giving us:

x+(x+4)=74

Simplifying gives us:

2x+4=74

-4 -4

---------

2x=70

--- ---

2 2

x=35

Since we now know that x=35, and we know that y=x+4, we now know that:

y=(35)+4

y=39

Now that we have both of the numbers, we should check our work to ensure it's correct:

Does 39+35=74? Yes it does.

Is 39 (the larger of the two numbers) four more than the smallest number (35)? Yes it is.

3 0

2 years ago

If y = 7.2 when x = 10, what is the value of x when y = 20? (y varies inversely as the square of x.)

Sphinxa [80]

The answer is 14.4.................................

4 0

3 years ago